Himmelblau’s function

\(f(x, y) = (x^{2} + y - 11)^{2} + (x + y^{2} - 7)^{2}\)

Local minima:

\(f(3.0, 2.0) = 0\)

\(f(-2.805118, 3.131312) = 0\)

\(f(-3.779310, -3.283186) = 0\)

\(f(3.584428, -1.848126) = 0\)

Eggholder function

\(f(x, y) = -(y + 47) \cdot sin(\sqrt{|y + \frac{x}{2} + 47}) - x \cdot sin(\sqrt{|x - (y + 47)|}\)

Global minimum: \((x, y) = (512, 404.2319)\)

Rastrigin function

\(f(x, y) = 20 + x^{2} - 10 \cdot cos(2 \pi x) + y^{2} - 10 \cdot cos(2 \pi y)\)

Global minimum: \((x, y) = (0, 0)\)

Schaffer function N. 2

\(f(x, y) = 0.5 + \frac{sin^{2}(x^{2}-y^{2}-0.5)}{[1 + 0.001\cdot(x^{2} + y^{2})]^{2}}\)

Global minimum: \((x, y) = (0, 0)\)

More

More test functions for optimization: https://en.wikipedia.org/wiki/Test_functions_for_optimization.